Yep, “The New Daughter’’ does tread with clunky boots upon well-worn horror movie territory. Every ominous sign is preceded by full moons, slithering fog, and thunderclaps.

Yet buried under a mound of haunted house cliches is a creepier, more sophisticated movie about the sexual power of teenage girls, and their fathers’ inability to comprehend, clambering to get out.

Despite the participation of Kevin Costner, few anticipated this under-the-radar supernatural thriller. Costner plays novelist John James, a soft-spoken, anti-action-hero, daunted by being a single dad. “How are you going to do this - be our father?’’ the daughter Louisa (Ivana Baquero) pouts. “You don’t have much practice.’’ (She also calls her mother a slut.)

Perhaps the Spanish director, Luis Alejandro Berdejo, hoped to steal some magic from Guillermo del Toro by casting Baquero, who played Ofelia in “Pan’s Labyrinth.’’ And he does have an eye for composing scenes; his static camera ratchets up the tension.

But around the time the younger brother spouts apropos lines about his ant farm needing a new queen, “The New Daughter’’ begins to fall apart. John gets advice from an old coot who knows the back story and warns him to get out of the house. Of course, Costner does not get out of the house. Berdejo’s camera veers into handheld, “Blair Witch’’ land. The beasts resemble wolfmen or worms or insects, depending on the scene. Their egg-sack “Alien’’ burrow looks as cheap as a carnival ride. By the final reel, Berdejo has undermined what he’s built.

There’s a more metaphorical and - far more disturbing - psychosexual film brewing here about parents’ failed promises to protect their children, and that infinite divide between fathers and daughters. For, above all, what befuddles John is Louisa’s transformation. She’s daddy’s little girl one moment and a door-slamming, “You ruin everything!’’ young woman the next. Her body is changing, and she tests that power every teenage girl learns to wield.

But then the tacky pod creatures get their close-up - as they always demand - and out comes the shotgun. At least the final sequence, rather than being redemptive, has the courage to be grim.